I'd have a discussion about your pain relief goals with your doctor. For example, if your pain levels have increased in recent months and you have pain spikes between the doses. Discuss what a reasonable pain level is and how you can get there. Its unreasonable to expect 100% relief, but 50% may be reasonable.

Discuss what kind of activities you are unable to accomplish currently. I wouldn't flat out ask for any specific med or even something long acting, but discuss some of the troubles you are having. What else are you doing for managing your pain besides the Percocet? Are you seeing a pain management specialist? That is something to push for if you have chronic pain. Best wishes.

Do not be aafraid to ask about a long acting medication. They do give a more steady pain relief and if you have constant pain, you will benefit from that. I take ms contin at bedtime, which is an extended release morphine and it last all night, so I dont have to get up in the middle of the night to take pain meds.
Most doctors are open to trying long acting meds because they are not like the short acting meds, where you feel them instantly. They just provide a more constant relief., some of them up to 12 hours. You can also stay on the percocets for break through pain, if needed.
I would just be open and honest with your doctor and ask is there something you can take that will give you pain relief, but doesnt have to be taken as often. Let him decide from there.
Good luck!